Amplification of short optical pulses in fiber amplifiers is limited by the onset of various nonlinear processes in the fiber. When conventional doped fibers based on fused silica are used for amplification of pulses, several meters of fiber are needed in order to reach sufficient levels of optical gain. Amplification in such long fibers typically results in severe spectral and temporal distortions that eventually lead to pulse breakup The breakup of an ultrashort pulse in a fiber amplifier for the case of anomalous dispersion, which is typical in Large-Mode Area (LMA) fibers at 1.5 μm wavelength, is illustrated in FIG. 1. These broken-up pulse waveforms, although may have appreciable total pulse energy, are of limited utility, because the peak power in these waveforms is limited, and these waveforms cannot be straightforwardly transformed into solitary pulses with high peak power.
There are several nonlinear effects that result in the pulse distortions in fiber amplifiers. Some of them can be more or less non-ambiguously quantified, while the others are not so easy to quantify. The quantifiable detrimental effects include self-phase modulation, Raman scattering, and self-focusing. The effects that are not as easily quantifiable but still very important are related to thermal issues in the amplifying fiber and potential damage to the output fiber end facet by the exiting high-energy laser pulses.
The degree of the nonlinear distortion of the amplified pulse due to self-phase modulation is quantified in terms of the so-called B-integral:
                              B          =                                                    2                ⁢                π                ⁢                                                                  ⁢                                  n                  2                                            λ                        ⁢                                          ∫                0                L                            ⁢                                                                    P                    ⁡                                          (                      z                      )                                                                                                  A                      core                                        ⁡                                          (                      z                      )                                                                      ⁢                                                                  ·                                  ⅆ                  z                                                                    ,                            (        1        )            
where n2=3×10−20 m2/W is the nonlinear refractive index of the fiber material (which is approximately the same for fused silica and other glasses that conventional optical fibers are made of), λ is the operation wavelength, Acore(z) is the area of the propagating mode in the fiber, and P(z) is the peak power of the amplified pulses. Both of the last two quantities are functions of z, the longitudinal coordinate along the fiber. The integration is carried out over the entire length of the amplifier, including the gain fiber and whatever length of passive fiber (if any) is connected to the output end of the gain fiber. Such passive fiber may be referred to as a fiber pigtail.
The maximum tolerable value of the B-integral at which the distorted pulses still maintain their shape and can be effectively compressed, is not strictly defined, and this maximum value depends on the exact temporal shape of the amplified pulses. However, more or less independently of the pulse shape, the nonlinear distortions associated with B-integrals of the order of 5 radians or more are, in general, unrecoverable. For the values of the B-integral exceeding this limit, the amplified pulses either breakup into several sub-pulses, or develop a large temporal pedestal. In both of the above cases, such pulses have a limited utility and their original shape cannot be effectively restored (i.e. the amplified pulses cannot be effectively re-compressed in time).
It is important to note that the dominant contribution to the B-integral comes from the end part of the gain fiber and from the entire length of any passive fiber connected to the output of the gain fiber. Connecting such passive fiber to the amplifier output is clearly detrimental to the amplifier operation, but still may be necessary for the purposes of reliable delivery of the amplified pulses or for pulse re-compression.
It is customary to define the so-called effective length of a fiber amplifier Leff such that the value of the B-integral in (1) can be re-written as:
                    B        =                                            2              ⁢              π              ⁢                                                          ⁢                              n                2                                                    λ              ⁢                                                          ⁢                              A                core                                              ⁢                                    P              out                        ·                          L              eff                                                          (        2        )            Leff=Leffgain+Lpigtail  (3)
In the formula (3) above, Leffgain is the effective length of the gain fiber, which, as pointed out above, is shorter than the entire length of the gain fiber, and Lpigtail is the entire length of the passive fiber connected to the output of the gain fiber (the pigtail). This definition implicitly implies that the effective area in the propagating lightwave is the same in the both gain fiber and the fiber pigtail. For fiber types that have different beam areas, the lengths Leffgain and Lpigtail in the formula (3) need to be weighed by factors proportional to the mode areas in the gain and fiber pigtail, respectively.
Several ways of mitigating the nonlinearity problem in pulsed fiber amplifiers have been developed in the past. From the above formula (3) for B-integral, the value of this integral (and consequently the severity of the nonlinear pulse distortions) can be reduced in three ways: by increasing the size of the propagating fiber mode, by decreasing the peak power of the pulses, and by reducing the effective length of the amplifier.
The area of the propagating fiber mode can be increased by using the so-called Large-Mode Area (LMA) fibers that can either be based on the conventional step-index geometry, or on various microstructure designs. Under certain conditions, multimode gain fibers can be used for the amplification of diffraction-limited optical signals. In the cases above, increasing the core size comes at a price of higher bending losses, and the maximum core size is ultimately limited by the degradation of the beam quality produced by the fiber-laser system. In addition, the mode coupling due to micro-bending from the fundamental to higher-order modes in a multimode LMA fiber grows rapidly with decreasing the outside fiber diameter. Consequently, in order to reduce the mode coupling, LMA fibers used for pulse amplification typically have outer diameters in excess of one millimeter. Such wide fibers may be referred to as “rod-type” fibers. “Rod-type” active fibers are stiff and in general are not pliable, which makes their integration into practical compact fiber-laser systems problematic.
Reducing the peak power of pulses inside the amplifier is the essence of the Chirped-Pulse Amplification (CPA) technique. In a CPA laser system, the pulses to be amplified are first stretched in time domain, which reduces their peak power. The stretched pulses are then amplified followed by their re-compression using free-space diffraction-grating compressors. This powerful approach is the workhorse of the modern high-energy laser technology, but applying this approach in a practical fiber amplifier system is not easy. The main limitation of the CPA technique as applied to fiber amplification, is associated with the limited choices for a pulse stretcher. Even though the generation of millijoule-level pulse energies in fiber-based CPA systems has been recently reported, stretching ratios of the order of 1:5000, as well as the necessity to carefully balance higher-order dispersion between stretcher and compressor, which is essential for operation of these systems, require bulky and cumbersome free-space stretcher/compressor arrangements.
Another approach of reducing the value of the B-integral is by reducing the effective length of the fiber amplifier. At a given doping concentration and core size of the amplifying fiber, the length of the amplifier determines the values of the optical gain and optical pulse power attainable from the amplification. For conventional doped fibers based on fused silica glass, the doping concentration is limited to a fraction of one percent (by weight). Accordingly, the typical length of large-mode area amplifiers made of these fibers is in the range from few to few tens of meters. The value of the peak pulse power attainable from such amplifiers is severely limited by the fiber nonlinearities and can be quantified by the formula (3) above. At the same time, packaging these amplifiers is relatively straightforward, as the meters-long gain fiber can be coiled and effectively cooled. FIG. 2 is an illustration of a large-mode area amplifier 110 with a gain fiber 112 coiled, as is known in the prior art. In addition, fused silica, the common material from which these fibers are made, is very hard and allows for an appropriate preparation of the exit facet of the amplifier (via end-face polishing, for example). Furthermore, since the gain fiber is several meters long, a dedicated passive fiber section can be added to the output of the gain fiber, without making the entire effective length of the amplifier substantially longer.
Recently, several new types of optical fibers have been developed. These fibers are made of special types of optical glasses that can be highly doped with rare-earth oxides. These novel fiber types include phosphate fibers and phospho-silicate glasses. The attainable doping concentrations in these glasses are, by at least an order of magnitude, higher compared to those in the conventional doped fibers made of fused silica glass. Due to the high concentration of doping in these glasses, the length of the fiber amplifier can be reduced, while maintaining the high values of the optical gain and output optical power. Thus by using short-lengths of these highly-doped fibers for amplification of optical pulses, the value of the B-integral can be reduced in proportion to the fiber length.
In spite of the clear advantages brought about by using short and highly doped fibers in pulse amplification applications, their use in practice is not straightforward. First, these fibers are typically inferior to fused silica in terms of mechanical rigidity and friendliness to common fiber-processing techniques. Second, in order to bring real advantage in terms of the reduced nonlinearity, the length of the gain fiber likely needs to be below fifty centimeters. At this short length, proper fiber preparation and packaging, as well as providing a proper arrangement for optical pumping the gain fiber become even more complicated.
Various optical pumping methods that have been developed for ordinary doped fibers have been adapted for use with highly-doped fibers. These doping methods include the core pumping via a wavelength-division-multiplexing (WDM) coupler, pumping through a groove cut in the side surface of the fiber, and side pumping via a multi-fiber arrangement that rely on the evanescent-field coupling between the active fiber and, in general, several passive pump-delivery fibers. FIG. 3 is an illustration of a side pumping arrangement 210 via multiple fibers that relies on the evanescent-field coupling between the active fiber 212 and the passive pump-delivery fibers 214, as is known in the prior art.
Thus, a heretofore unaddressed need exists in the industry to address the aforementioned deficiencies and inadequacies.